Question

Which of the following shows the correct steps to find the value of 8 to the power of 1 over 3?

Answer 1

Among the choices the correct steps to find the value of 8 to the power of 1 over 3 is the second one which is 8 to the power of 1 over 3 equals 2 to the power of 3 whole to the power of 1 over 3 equals 2 to the power of 3 multiplied by 1 over 3 equals 2. 

Answer 2

The correct answer is:

8 to the power of 1 over 3 equals 2 to the power of 3 whole to the power of 1 over 3 equals 2 to the power of 3 multiplied by 1 over 3 equals 2

Explanation:

We are asked to evaluate $8^{\frac{1}{3}}$. We know that if we raise a power to a power, we simplify it by multiplying the exponents; this will create a whole number exponent if we can rewrite 8 as a number to the 3rd power.

8 = 2(2)(2) = 2³

This means

$8^{\frac{1}{3}}=(2^3)^{\frac{1}{3}}=2^{3\times \frac{1}{3}}=2^{\frac{3}{3}}=2^1=2$